Find an equation of the line through the point (2, 1) that cuts off the least area
from the first quadrant.
The line must satisfy f(2) = 1, so the slope and y-intercept will vary. We want the minimum area.
with ,
and
Therefore...
We want to minimize the area of the 1st quadrant or the area of y-intercept * x-intercept
The x-intercept is when y=0
The y-intercept is just b
b = 1-2m
Area must be equal to:
Find the derivative and set equal to zero...
Slope must equal -0.5 since a positive slope will give an infinite area in the 1st quadrant...
AREA: